General Topology-I

Impulsive Differential Equations

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On Fixed Points

In this paper, we define soft ω -open sets and strongly soft ω -open sets as two new classes of soft sets. We study the natural properties of these types of soft sets and we study the validity of the exact versions of some known results in ordinary topological spaces regarding ω -open sets in soft topological spaces. Also, we study the relationships between the ω -open sets of a given indexed family of topological spaces and the soft ω -open sets (resp. strongly soft ω -open sets) of their generated soft topological space. These relationships form a biconditional logical connective which is a symmetry. As an application of strongly soft ω -open sets, we characterize soft Lindelof (resp. soft weakly Lindelof) soft topological spaces.

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On Two Classes of Soft Sets in Soft Topological Spaces

In the present paper, some sufficient conditions for closed mappings to be peripherally compact are given and a problem of Y. Tanaka and C. Liu is answered.

On Closed Mappings

On some generated soft topological spaces and soft homogeneity.

In various articles, it is said that the class of all soft topologies on a common universe forms a complete lattice, but in this paper, we prove that it is a complete lattice. Some soft topologies are maximal, and some are minimal with respect to specific soft topological properties. We study the properties of soft compact and soft connected topologies that are maximal. Particularly, we prove that a maximal soft compact topology has identical families of soft compact and soft closed sets. We further show that a maximal soft compact topology is soft T1, while a maximal soft connected topology is soft T0. Lastly, we establish that each soft connected relative topology to a maximal soft connected topology is maximal.

Maximal Soft Compact and Maximal Soft Connected Topologies

Strong Form of Soft Semi-Open Sets in Soft Topological Spaces

We extend the notion of omega open set in ordinary topological spaces to generalized topological spaces. We obtain several characterizations of omega open sets in generalized topological spaces and prove that they form a generalized topology. Using omega open sets we introduce characterizations of Lindelöf, compact, and countably compact concepts generalized topological spaces. Also, we generalize the concepts of continuity in generalized topological spaces via omega open sets. c ©2016 All rights reserved.

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Samer Al Ghour

Papers

On Two Classes of Soft Sets in Soft Topological Spaces

On some generated soft topological spaces and soft homogeneity.

Maximal Soft Compact and Maximal Soft Connected Topologies

Strong Form of Soft Semi-Open Sets in Soft Topological Spaces

Omega open sets in generalized topological spaces